Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

新生大鼠脊髓薄片交感节前神经元的长时程后超极化电位

在新生大鼠胸腰段脊髓薄片,对经腹根逆行刺激鉴定的交感节前神经元（ＳＰＮｓ）进行细胞内记录．发现部分ＳＰＮｓ有长时程后超极化电位（１１－ＳＨＰ）,其达峰时间为０．２－０．７ｓ．时程１－１０ｓ,幅度７－２０ｍＶ。１１－ＡＨＰ前部常为６—３０ｍｓ达峰、短于４００ｍｓ时程的快ＡＨＰ成分。１１－ＡＨＰ除伴有膜输入电阻降低外,还呈膜电位依赖性,翻转电位为－９０至－１００ｍＶ。结果证明１１－ＡＨＰ能起着控制ＳＰＮ的放电频率的重要作用。     

Dependence of different spike sequences on the mean neuronal firing rate in the neocortex in vivo and in vitro

Neuronal spikes were recorded extracellularly in rabbit visual cortex in vivo (88 cells) and in surviving slices of guinea pig sensorimotor cortex in vitro (50 cells). Spike sequences (SS) with monotonically increasing (SS+) and decreasing (SS-) interspike intervals were detected. Relative number of spikes of SS in the recording was closely associated with SS generation. The relative number of spikes was plotted against the average firing rate, this function had a biphasic character with the critical point around 7 Hz. The rate of change in interspike duration (the slope) was virtually independent of the firing rate, but was significantly different in vivo and in vitro conditions for both SS+ (325 and 180 ms/s, respectively) and SS- (270 and 160 ms/s, respectively). By and large, in vivo and in vitro the spike sequence parameters depended in the average firing rate in the same manner. The role of the spike sequences in rhythmic and information processes in neocortex is discussed.     

Motor unit activity and surface electromyogram power spectrum during increasing force of contraction

Twelve male subjects were tested to determine the relationship between motor unit (MU) activities and surface electromyogram (EMG) power spectral parameters with contractions increasing linearly from zero to 80% of maximal voluntary contraction (MVC). Intramuscular spike and surface EMG signals recorded simultaneously from biceps brachii were analyzed by means of a computer-aided intramuscular MU spike amplitude-frequency (ISAF) histogram and an EMG frequency power spectral analysis. All measurements were made in triplicate and averaged. Results indicate that there were highly significant increases in surface EMG amplitude (71 +/- 31.3 to 505 +/- 188 microV, p less than 0.01) and mean power frequency (89 +/- 13.3 to 123 +/- 23.5 Hz, p less than 0.01) with increasing force. These changes were accompanied by progressive increases in the firing frequency of MU's initially recruited, and of newly recruited MU's with relatively larger spike amplitudes. The group data in the ISAF histograms revealed significant increases in mean spike amplitude (412 +/- 79 to 972 +/- 117 microV, p less than 0.01) and mean firing frequency (17.8 +/- 5.4 to 24.7 +/- 4.1 Hz, p less than 0.01). These data suggest that surface EMG spectral analysis can provide a sensitive measure of the relative changes in MU activity during increasing force output.     

Alterations in the Intrinsic Burst Activity of Purkinje Neurons in Offspring Maternally Exposed to the CB1 Cannabinoid Agonist WIN 55212-2

Burst firing plays an important role in normal neuronal function and dysfunction. In Purkinje neurons, where the firing rate and discharge pattern encode the timing signals necessary for motor function, any alteration in firing properties, including burst activity, may affect the motor output. Therefore, we examined whether maternal exposure to the cannabinoid receptor agonist WIN 55212-2 (WIN) may affect the burst firing properties of cerebellar Purkinje cells in offspring. Whole-cell somatic patch-clamp recordings were made from cerebellar slices of adult male rats that were exposed to WIN prenatally. WIN exposure during pregnancy induced long-term alterations in the burst firing behavior of Purkinje neurons in rat offspring as evidenced by a significant increase in the mean number of spikes per burst (p < 0.05) and the prolongation of burst firing activity (p < 0.01). The postburst afterhyperpolarization potential (p < 0.001), the mean intraburst interspike intervals (p < 0.001) and the mean intraburst firing frequency (p < 0.001) were also significantly increased in the WIN-treated group. Prenatal exposure to WIN enhanced the firing irregularity as reflected by a significant decrease in the coefficient of variation of the intraburst interspike interval (p < 0.05). Furthermore, whole-cell voltage-clamp recordings revealed that prenatal WIN exposure significantly enhanced Ca²⁺ channel current amplitude in offspring Purkinje neurons compared to control cells. Overall, the data presented here strongly suggest that maternal exposure to cannabinoids can induce long-term changes in complex spike burst activity, which in turn may lead to alterations in neuronal output.     

Picosecond Pulse Electrical Field Suppressing Spike Firing in Hippocampal CA1 in Rat In Vivo

Picosecond pulse electrical fields (psPEFs), due to their high temporal-resolution accuracy and localization, were viewed as a potential targeted and noninvasive method for neuromodulation. However, few studies have reported psPEFs regulating neuronal activity in vivo. In this paper, a preliminary study on psPEFs regulating action potentials in hippocampus CA1 of rats in vivo was carried out. By analyzing the neuronal spike firing rate in hippocampus CA1 pre- and post-psPEF stimulation, effects of frequency, duration, and dosimetry of psPEFs were studied. The psPEF used in this study had a pulse width of 500 ps and a field strength of 1 kV/mm, established by 1 kV picosecond voltage pulses. Results showed that the psPEF suppressed spike firing in hippocampal CA1 neurons. The suppression effect was found to be significant except for 10 s, 10 Hz. For short-duration stimulation (10 s), the inhibition rate of spike firing increased with frequency. At longer stimulation durations (1 and 2 min), the inhibition rate increased and decreased alternately as the frequency increased. Despite this, the inhibition rate at high frequencies (5 and 10 kHz) was significantly larger than that at 10 and 100 Hz. A cumulative effect of psPEF on spike firing inhibition was found at low frequencies (10 and 100 Hz), which was saturated when frequency reached 500 Hz or higher. This paper conducts a study on psPEF regulating spike firing in hippocampal CA1 in vivo for the first time and guides subsequent study on psPEF achieving noninvasive neuromodulation. © 2020 Bioelectromagnetics Society     

新生大鼠离体脊髓薄片侧角中间外侧核细胞的电生理特性

在新生大鼠离体脊髓薄片的中间外侧核作细胞内记录,研究细胞膜的静态与动态电生理特性。细胞的静息电位(RP)变动于-46—-70mV,膜的输入阻抗为108.3±67.9MΩ(X±SD,下同),时间常数9.9±5.6ms,膜电容138.6±124.2pF。用去极化电流进行细胞内刺激时,大部份细胞(85.4％)能产生高频率连续发放,其余细胞(15.6％)仅产生初始单个发放。胞内直接刺激引起的动作电位(AP)幅度为63.4±9.0mV,时程2.4±0.6ms,阈电位水平在RP基础上去极18.7±6.2mV。大部份细胞的锋电位后存在明显的超极化后电位,其幅度为5.1±2.7mV、持续90±31.8ms。刺激背根可在记录细胞引起EPSP或顺向AP,少数细胞尚出现IPSP。而刺激腹根则可引起逆向AP。     

Intramuscular and surface electromyogram changes during muscle fatigue

Twelve male subjects were tested to determine the effects of motor unit (MU) recruitment and firing frequency on the surface electromyogram (EMG) frequency power spectra during sustained maximal voluntary contraction (MVC) and 50% MVC of the biceps brachii muscle. Both the intramuscular MU spikes and surface EMG were recorded simultaneously and analyzed by means of a computer-aided intramuscular spike amplitude-frequency histogram and frequency power spectral analysis, respectively. Results indicated that both mean power frequency (MPF) and amplitude (rmsEMG) of the surface EMG fell significantly (P less than 0.001) together with a progressive reduction in MU spike amplitude and firing frequency during sustained MVC. During 50% MVC there was a significant decline in MPF (P less than 0.001), but this decline was accompanied by a significant increase in rmsEMG (P less than 0.001) and a progressive MU recruitment as evidenced by an increased number of MUs with relatively large spike amplitude. Our data suggest that the surface EMG amplitude could better represent the underlying MU activity during muscle fatigue and the frequency powers spectral shift may or may not reflect changes in MU recruitment and rate-coding patterns.     

Pharmacological and molecular enhancement of learning in aging and Alzheimer's disease.

When animals learn hippocampus-dependent associative and spatial tasks such as trace eyeblink conditioning and the water maze, CA1 hippocampal neurons become more excitable as a result of reductions in the post-burst, slow afterhyperpolarization. The calcium-activated potassium current that mediates this afterhyperpolarization is activated by the calcium influx that occurs when a series of action potentials fire and serves as a modulator of neuronal firing frequency. As a result, spike frequency accommodation is also reduced after learning. Neuronal calcium buffering processes change and/or voltage-dependent calcium currents increase during aging; leading to enhancements in the slow afterhyperpolarization, increased spike frequency accommodation and age-associated impairments in learning. We describe a series of studies done to characterize this learning-specific enhancement in intrinsic neuronal excitability and its converse in aging brain. We have also combined behavioral pharmacology and biophysics in experiments demonstrating that compounds that increase neuronal excitability in CA1 pyramidal neurons also enhance learning rate of hippocampus-dependent tasks, especially in aging animals. The studies reviewed here include those using nimodipine, an L-type calcium current blocker that tends to cross the blood-brain barrier; metrifonate, a cholinesterase inhibitor; CI1017, a muscarinic cholinergic agonist; and galantamine, a combined cholinesterase inhibitor and nicotinic agonist. Since aging is the chief risk factor for Alzheimer's disease, a disease that targets the hippocampus and associated brain regions and markedly impairs hippocampus-dependent learning, these compounds have potential use as treatments for this disease. Galantamine has been approved by the USDA for this purpose. Finally, we have extended our studies to the TG2576 transgenic mouse model of Alzheimer's disease (AD), that overproduces amyloid precursor protein (APP) and increases levels of toxic beta-amyloid in the brain. Not only do these mice show deficits in hippocampus-dependent learning as they age, but their hippocampal neurons show a reduced capacity to increase their levels of intrinsic excitability with reductions in the slow afterhyperpolarization after application of the muscarinic agonist carbachol. These TG2576 APP overproducing mice were crossed with BACE1 knockout mice, that do not produce beta-amyloid because cleavage of APP by the beta-site APP cleaving enzyme 1 (BACE1) is a critical step in its formation. Not only was hippocampus-dependent learning rescued in the bigenic TG2576-BACE1 mice, but the capacity of hippocampal neurons to show normal enhancements of intrinsic excitability was restored. The series of studies reviewed here support our hypothesis that enhancement in intrinsic excitability by reductions in calcium-activated potassium currents in hippocampal neurons is an important cellular mechanism for hippocampus-dependent learning.     

Afterpotentials and transduction properties in different types of central neurones

In mammalian central neurones, the soma-dendritic spike is generally followed by afterpotentials, a brief depolarizing potential (delayed depolarization) and a more longlasting afterhyperpolarization (AHP). These afterpotentials, and in particular the AHP, have long been considered as important factors in the control of excitation-to-frequency transduction. Analysis of the afterpotential properties has been performed on various types of central neurones; spinal alpha-motoneurones, dorsal spinocerebellar tract cells, rubrospinal neurones and hippocampal CA1 pyramidal cells. These investigations have shown the afterpotentials to differ considerably in their characteristics among these types of neurones. Studies of the firing behaviour of the neurones have also shown great variations in their firing properties, the observed differences being well in accord with those expected on the basis of their different afterpotential characteristics. The results suggest that the afterpotentials play a major role in the control of excitation-to-frequency transduction in several types of central neurones.     

Serotonin increases excitability of rabbit C-fiber neurons by two distinct mechanisms

Serotonin (5-HT) increases impulse activity in visceral afferent C-fibers in vivo. A 5-HT-induced membrane depolarization may partially account for this effect. Here, we examined the potential contribution of an additional mechanism to the 5-HT-mediated increase in impulse activity. Approximately 40% of rabbit visceral C-fiber neurons exhibit a protracted (greater than 3 s) spike afterhyperpolarization (AHPslow) that is a major determinant of repetitive firing properties in these neurons. Intracellular recording methods were applied to rabbit nodose ganglion neurons in vitro to assess whether 5-HT could increase excitability through effects on the AHPslow. Results revealed a concentration-dependent 5-HT-mediated depression of the AHPslow amplitude and duration that was accompanied by decreased accommodation of action potential firing. Experiments with 5-HT receptor antagonists further showed that this autacoid depressed the AHPslow through a different 5-HT receptor subtype than that subserving the 5-HT-induced depolarization. Thus the AHPslow represents a distinct locus where 5-HT can increase the impulse activity of these visceral C-fiber afferents.     

Profound alterations in the intrinsic excitability of cerebellar Purkinje neurons following neurotoxin 3-acetylpyridine (3-AP)-induced ataxia in rat: new insights into the role of small conductance K+ channels

Alterations in the intrinsic properties of Purkinje cells (PCs) may contribute to the abnormal motor performance observed in ataxic rats. To investigate whether such changes in the intrinsic neuronal excitability could be attributed to the role of Ca(2+)-activated K(+) channels (K(Ca)), whole cell current clamp recordings were made from PCs in cerebellar slices of control and ataxic rats. 3-AP induced profound alterations in the intrinsic properties of PCs, as evidenced by a significant increase in both the membrane input resistance and the initial discharge frequency, along with the disruption of the firing regularity. In control PCs, the blockade of small conductance K(Ca) channels by UCL1684 resulted in a significant increase in the membrane input resistance, action potential (AP) half-width, time to peak of the AP and initial discharge frequency. SK channel blockade also significantly decreased the neuronal discharge regularity, the peak amplitude of the AP, the amplitude of the afterhyperpolarization and the spike frequency adaptation ratio. In contrast, in ataxic rats, both the firing regularity and the initial firing frequency were significantly increased by the blockade of SK channels. In conclusion, ataxia may arise from alterations in the functional contribution of SK channels, to the intrinsic properties of PCs.     

Contribution of Dopamine D1/5 Receptor Modulation of Post-Spike/Burst Afterhyperpolarization to Enhance Neuronal Excitability of Layer V Pyramidal Neurons in Prepubertal Rat Prefrontal Cortex

Dopamine (DA) receptors in the prefrontal cortex (PFC) modulate both synaptic and intrinsic plasticity that may contribute to cognitive processing. However, the ionic basis underlying DA actions to enhance neuronal plasticity in PFC remains ill-defined. Using whole-cell patch-clamp recordings in layer V-VI pyramidal cells in prepubertal rat PFC, we showed that DA, via activation of D1/5, but not D2/3/4, receptors suppress a Ca²⁺-dependent, apamin-sensitive K⁺ channel that mediates post-spike/burst afterhyperpolarization (AHP) to enhance neuronal excitability of PFC neurons. This inhibition is not dependent on HCN channels. The D1/5 receptor activation also enhanced an afterdepolarizing potential (ADP) that follows the AHP. Additional single-spike analyses revealed that DA or D1/5 receptor activation suppressed the apamin-sensitive post-spike mAHP, further contributing to the increase in evoked spike firing to enhance the neuronal excitability. Taken together, the D1/5 receptor modulates intrinsic mechanisms that amplify a long depolarizing input to sustain spike firing outputs in pyramidal PFC neurons.     

Augmentation and suppression of action potentials by estradiol in the myometrium of pregnant rat.

The purpose of this study was to investigate the actions of estradiol on spontaneous and evoked action potentials in the isolated longitudinal smooth muscle cells of the pregnant rat. Single cells were obtained by enzymatic digestion from pregnant rat longitudinal myometrium. Action potentials and currents were recorded by whole-cell current-clamp and voltage-clamp methods, respectively. The acute effects of 17beta-estradiol on action potentials and inward and outward currents were investigated. The following results were obtained. The average resting membrane potential of single myometrial cells was -54 mV (n = 40). In many cells, an electrical stimulation evoked a membrane depolarization, and action potentials were superimposed on the depolarization. In some cells, spontaneous action potentials were observed. Estradiol (30 microM) slightly depolarized the membrane (ca. 5 mV) and attenuated the generation of action potentials by reducing the frequency and amplitude of the spikes. Afterhyperpolarization was also attenuated by estradiol (30 microM). On the other hand, in 5 of 35 cells, estradiol increased the first spike amplitude and action potential duration, while frequency of the spike generation and afterhyperpolarization were inhibited. In voltage-clamped muscle cells, estradiol inhibited both inward and outward currents. Acute inhibition or augmentation of spike generation by estradiol is due to the balance of inhibition of inward and outward currents. Inhibition of both currents also prevented afterhyperpolarization, causing potential-dependent block of Ca spikes.     

Stochastically Gating Ion Channels Enable Patterned Spike Firing through Activity-Dependent Modulation of Spike Probability

The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.     

Electrophysiological characteristics of reticulospinal neurones in relation to the conduction velocity of their axons

Activity was recorded intracellularly from the bodies of 87 reticulospinal neurones in the cat's gigantocellular nucleus, whose axons had a conduction velocity of 18-148 m.s-1. Slow-conducting neurones (18-45 m.s-1, 23%) were characterized by a wider action potential, higher input resistance (3.8-7.0 M omega) and a lower rheobase (1.0-1.7 nA). They were also very sensitive to changes in membrane polarity and generated regular rhythmic activity. Fast-conducting neurons (45-148 m.s-1) were characterized by a short action potential, low input resistance (0.7-2.9 M omega) and a higher rheobase (1.5-5.2 nA). When depolarizing current pulses were applied, they generated responses with action potentials with a high frequency, especially in the initial phase of depolarization, but their thresholds for the initiation of activity and steady firing were higher than in the case of slow neurones. Slow reticulospinal neurones always responded to stimulation of the spinal funiculi (mainly the dorsal funiculus) by a characteristic large postsynaptic potential on which large numbers of spike potentials were superimposed and which did not occur in fast neurones. The differences observed in membrane properties and in the character of generation of action potentials draw attention to the phasic character of fast, and the tonic character of slow, reticulospinal neurones.     

Electrical properties of neurons recorded from the rat supraoptic nucleus in vitro

The electrical properties of neurons in the supraoptic nucleus (so.n.) have been studied in the hypothalamic slice preparation by intracellular and extracellular recording techniques, with Lucifer Yellow CH dye injection to mark the recording site as being the so.n. Intracellular recordings from so.n. neurons revealed them to have an average membrane potential of -67 +/- 0.8 mV (mean +/- s.e.m.), membrane resistance of 145 +/- 9 M omega with linear current-voltage relations from 40 mV in the hyperpolarizing direction to the level of spike threshold in the depolarizing direction. Average cell time constant was 14 +/- 2.2 ms. So.n. action potentials ranged in amplitude from 55 to 95 mV, with a mean of 76 +/- 2 mV, and a spike width of 2.6 +/- 0.5 ms at 30% of maximal spike height. Both single spikes and trains of spikes were followed by a strong, long-lasting hyperpolarization with a decay fitted by a single exponential having a time constant of 8.6 +/- 1.8 ms. Action potentials could be blocked by 10(-6) M tetrodotoxin. Spontaneously active so.n. neurons were characterized by synaptic input in the form of excitatory and inhibitory postsynaptic potentials, the latter being apparently blocked when 4 M KCl electrodes were used. Both forms of synaptic activity were blocked by application of divalent cations such as Mg2+, Mn2+ or Co2+. 74% of so.n. neurons fired spontaneously at rates exceeding 0.1 spikes per second, with a mean for all cells of 2.9 +/- 0.2 s-1. Of these cells, 21% fired slowly and continuously at 0.1 - 1.0 s-1, 45% fired continuously at greater than 1 Hz, and the remaining 34% fired phasically in bursts of activity followed by silence or low frequency firing. Spontaneously firing phasic cells showed a mean burst length of 16.7 +/- 4.5 s and a silent period of 28.2 +/- 4.2 s. Intracellular recordings revealed the presence of slow variations in membrane potential which modified the neuron's proximity to spike threshold, and controlled phasic firing. Variations in synaptic input were not observed to influence firing in phasic cells.     

Influence of motoneuron firing synchronization on SEMG characteristics in dependence of electrode position.

The frequency content of the surface electromyography (SEMG) signal, expressed as median frequency (MF), is often assumed to reflect the decline of muscle fiber conduction velocity in fatigue. MF also decreases when motor unit firings synchronize, and we hypothesized that this effect can explain the electrode-dependent pattern in our previous recordings from the trapezius muscle. An existing motoneuron (MN) model describes the afterhyperpolarization following a spike as an exponential function on which membrane noise is superimposed. Splitting the noise into a common and an individual component extended the model to a MN pool with a tunable level of firing synchrony. An analytical volume conduction model was used to generate motor unit action potentials to simulate SEMG. A realistic level of synchrony decreased the MF of the simulated bipolar SEMG by approximately 30% midway between endplate position and tendon but not above the endplate. This is in accordance with experimental data from the biceps brachii muscle. It was concluded that the pattern of decrease of MF during sustained contractions indeed reflects MN synchronization.     

Firing rhythmicity in the neocortex in vivo and in vitro under sustained iontophoretic excitation

Extracellular recordings were made from the cat intact neocortex and guinea-pig neocortical slices during microiontophoretic application of amino acid neurotransmitters. Spike train autocorrelation analysis showed a high stability of firing patterns in the intact neocortex. When excitation of a cell was increased in a step-wise manner with glutamate iontophoresis only an enhancement of the rate of firing was observed. The rhythmic component, which was mainly due to periodic multiple discharges, remained up to the highest firing frequencies. In contrast to the in vivo observation, glutamate, aspartate or K⁺ iontophoresis in cortical slices resulted in firing pattern alternations (always from bursts or irregular activity to regular spike firing) as well as an increase in firing rate. In slices the periodic component was typically due to single-spike regularity and its frequency rose with an increase of firing rate. The comparison of autocorrelogram alternations in vivo and in vitro suggests that the temporal organization of spike trains in the intact cortex is under tight external control and is defined mainly by neuronal interactions, whereas virtually all the neurons in vitro are very sensitive to the same iontophoretic influences and their individual outputs easily change according to the excitation (depolarization) level. The coincidence of the lowest frequencies of single-spike regularity in the in vitro preparation (5–7 Hz and 8–10 Hz) with theta- and alpha-rhythms in the electroencephalogram (EEG), and with single unit firing rhythmicity in the whole brain, may represent the basis of a unit-circuit resonance and provide a high stability of these EEG-rhythms.Abbreviations ACF autocorrelation function - BFA background firing activity - EEG electroencephalogram     

A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing patterns of single neurons

We introduce a stochastic spike train analysis method called joint interspike interval difference (JISID) analysis. By design, this method detects changes in firing interspike intervals (ISIs), called local trends, within a 4-spike pattern in a spike train. This analysis classifies 4-spike patterns that have similar incremental changes. It characterizes the higher-order serial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint distribution of consecutive changes in ISIs, from which the serial dependence of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint distribution of consecutive ISI differences (ISIDs) is quantified. The graphical location of points in the JISID scatter plot reveals the local trends in firing (i.e., monotonically increasing, monotonically decreasing, or transitional firing). The trajectory of these points in the serial-JISID plot traces the time evolution of these trends represented by a 5-spike pattern, while points in the JISID scatter plot represent trends of a 4-spike pattern. We provide complete theoretical interpretations of the JISID analysis. We also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons. Received: 13 May 1997 / Accepted in revised form: 9 December 1998